Mane, who came on as a late substitute in the 1-1 draw, was seen gesticulating at Klopp on the pitch after the final whistle
Klopp though has played down the incident and said that the heated discussion was about the formation.
“It is not a big thing,” said Klopp, insisting the matter was about positioning. “We could have done it in the dressing room. Everything was sorted immediately.”
Klopp meanwhile was angry afterwards, claiming referee Michael Oliver refused to let him make a substitution prior to Chelsea’s crucial equaliser at Anfield.
Substitute Willian secured a 1-1 draw for the Premier League champions on Saturday when he lobbed Simon Mignolet from a tight angle in the 85th minute.
Liverpool had seemed on course for victory after taking the lead through former Chelsea forward Mohamed Salah after 65 minutes.
Klopp claimed he wanted to introduce Adam Lallana and change his team’s shape to protect the lead but said he was made to wait by Oliver.
Klopp told BT Sport: “I was angry because we wanted to change the system but the ref didn’t give us the opportunity. I don’t know what he thought in this moment, he told me something about taking too long, I don’t understand it.
“How can we take too long? We didn’t want to time waste, we wanted to change the system and that’s why I was angry.”
He added in his post-match press conference: “In my mind Ragnar Klavan would have been exactly in the position where Willian crossed the ball. Maybe we would have blocked the cross. So, it doesn’t feel too well when we couldn’t change the system.
Klopp also thought Willian’s late effort was unintentional.
He said: “Everything was good until Willian crossed the ball. Most parts of the game were good but it doesn’t feel it.
“But that is how it is. We will be better. The world is a strange and a crazy place at the moment so I can easily live with a point against Chelsea.
“It was a good game, an intense game and a very difficult game against a strong Chelsea team.”
